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M.; Einstufige Verfahren zur Fl\"achenapproximation unregel\-m\"assig verteilter Daten durch Tensor--Produkt--B--Splines; hahn-Meitner Institute, Berlin; 1985; %SchmidtR88 \rhl{S} \refR Schmidt, R.; Formerhaltende Interpolation; Angewandte Informatik, 177--180; 1988; %SchmidtRSteinVidic76 \rhl{S} \refR Schmidt, R., Stein, D., Vidic, C.; Linearer Ausgleich diskreter Daten mit dem interaktiven Programm LINFIT; Hahn-Meitner; 1976; %SchmidtRSteinfeld86a % . \rhl{S} \refR Schmidt, R. M., Steinfeld, M.; Die Konstruktion von stetig differenzierbaren Fl\"achen zur Interpolation unregelm\"assig verteilter Daten; Rpt.\ HMI-B371, Hahn-Meitner-Institut (Berlin); 1986; %SchmidtWalther97 % carl 26aug98 \rhl{S} \refP Schmidt, J., Walther, M.; Gridded data interpolation with restrictions on the first orde derivatives; \Mannheimnisi; 289--306; %Schneider93 % larry \rhl{S} \refD Schneider, F.-J.; Interpolation, Approximation und Konvertierung mit rationalen B-Splines; Darmstadt; 1993; %SchneiderKobbelt00 % larry 20apr00 \rhl{} \refP Schneider, R., Kobbelt, L.; Discrete fairing of curves and surfaces based on linear curvature distribution; \Stmalod; 371--380; %SchneiderWerner86 % . 14may99 \rhl{S} \refJ Schneider, C., Werner, W.; Some new aspects of rational interpolation; \MC; xx; 1986; xxx--xxx; % derivative of polynomial interpolant in barycentric form %Schoenberg34a % carl 02feb01 \rhl{S} \refJ Schoenberg, I. J.; Zur Abz\"ahlung der reellen Wurzeln algebraischer Gleichungen; \MZ; 38; 1934; 546--564; % %Schoenberg35a \rhl{S} \refJ Schoenberg, I. J.; Remarks to Maurice Fr\'echet's article `Sur la d\'efinition axiomatique d'une classe d'espace distanci\'es vectoriellement applicable sur l'espace de Hilbert'; Ann.\ Math.; 36; 1935; 724--732; %Schoenberg37a % carl \rhl{S} \refJ Schoenberg, I. J.; On certain metric spaces arising from Euclidean spaces by a change of metric and their imbedding in Hilbert space; Ann.\ Math.; 38(4); 1937; 787--793; %Schoenberg38a % carl \rhl{S} \refJ Schoenberg, I. J.; Metric spaces and completely monotone functions; Ann.\ Math.; 39(4); 1938; 811--841; %Schoenberg38b % carl \rhl{S} \refJ Schoenberg, I. J.; Metric spaces and positive definite functions; \TAMS; 44; 1938; 522--536; %Schoenberg42 % . \rhl{S} \refJ Schoenberg, I. J.; Positive definite functions on spheres; \DMJ; 9; 1942; 96--108; %Schoenberg46a % larry \rhl{S} \refJ Schoenberg, I. J.; Contributions to the problem of approximation of equidistant data by analytic functions, Part A: On the problem of smoothing or graduation, a first class of analytic approximation formulas; Quart.\ Appl.\ Math.; 4; 1946; 45--99; %Schoenberg46b \rhl{S} \refJ Schoenberg, I. J.; Contributions to the problem of approximation of equidistant data by analytic functions, Part B: On the problem of osculatory interpolation, a second class of analytic approximation formulae; Quart.\ Appl.\ Math.; 4; 1946; 112--141; %Schoenberg48a % . 21feb96 \rhl{S} \refJ Schoenberg, I. J.; On variation-diminishing integral operators of the convolution type; \PNAS; 34; 1948; 164--169; %Schoenberg58 % larry \rhl{S} \refJ Schoenberg, I. J.; Spline functions convex curves and mechanical quadratures; \BAMS; 64; 1958; 352--357; %Schoenberg59 \rhl{S} \refP Schoenberg, I. J.; On variation diminishing approximation methods; \Langer; 249--274; %Schoenberg64 % Elisabeth \rhl{S} \refJ Schoenberg, I. J.; On best approximations of linear operators; Indag.\ Math.; 26; 1964; 155--163; % Koninkl.\ Ned.\ Akad.\ Wetenschap.\ Proc.\ Ser.\ A: 67: 1964: 155--163: %Schoenberg64b \rhl{S} \refQ Schoenberg, I. J.; On interpolation by spline functions and its minimal properties; (On Approximation Theory (Proc.\ Oberwolfach Conf.\ 4--10 Aug, 1963)), P. L. Butzer and J. Korevaar (eds.), ISNM Vol.\ 5, Birkh\"auser (Basel); 1964; 109--129; %Schoenberg64c % larry \rhl{S} \refJ Schoenberg, I. J.; Spline interpolation and the higher derivatives; \PNAS; 51; 1964; 24--28; %Schoenberg64d % larry \rhl{S} \refJ Schoenberg, I. J.; Spline interpolation and best quadrature formulae; \BAMS; 70; 1964; 143--148; %Schoenberg64e % carl \rhl{S} \refJ Schoenberg, I. J.; On trigonometric spline interpolation; \JMM; 13(5); 1964; 795--825; %Schoenberg64g \rhl{S} \refJ Schoenberg, I. J.; Spline functions and the problem of graduation; \PAMS; 52; 1964; 947--950; %Schoenberg65a % larry \rhl{S} \refJ Schoenberg, I. J.; On monosplines of least deviation and best quadrature formulae; \SJNA; 2; 1965; 144--170; %Schoenberg65b % . 19may96 \rhl{S} \refR Schoenberg, I. J.; Letter to Philip J. Davis; 31 May; 1965; %Schoenberg66a % larry \rhl{S} \refJ Schoenberg, I. J.; On monosplines of least deviation and best quadrature formulae II.; \SJNA; 3; 1966; 321--328; %Schoenberg66b \rhl{S} \refJ Schoenberg, I. J.; On Hermite-Birkhoff interpolation; \JMAA; 16; 1966; 538--543; % renewed interest in Birkhoff interpolation; intro of `poised' even though % already Polya31 had used `normal', as had BirkhoffGD06 %Schoenberg67a % larry \rhl{S} \refQ Schoenberg, I. J.; On spline functions (with a supplement by T. N. E. Greville); (Inequalities I), O. Shisha (ed.), Academic Press (New York); 1967; 255--291; %Schoenberg68a \rhl{S} \refQ Schoenberg, I. J.; Spline interpolation and the higher derivatives; (Abhandlungen aus Zahlentheorie und Analysis), P. Turan (ed.), Deutscher Verlag der Wissenschaften (Berlin); 1968; 279--295; % cf Schoenberg69b %Schoenberg68b \rhl{S} \refJ Schoenberg, I. J.; On spline interpolation at all integer points of the real axis; Matematica (Cluj); 10; 1968; 151--170; %Schoenberg68c \rhl{S} \refJ Schoenberg, I. J.; On the Ahlberg-Nilson extension of spline interpolation: the g-splines and their optimal properties; \JMAA; 21; 1968; 207--231; %Schoenberg69a % larry \rhl{S} \refP Schoenberg, I. J.; Monosplines and Quadrature Formulae; \MadisonI; 157--207; %Schoenberg69b \rhl{S} \refQ Schoenberg, I. J.; Spline interpolation and the higher derivates; (Number Theory and Analysis), xxx (ed.), Plenum (New York); 1969; 279--295; % isn't this the same as Schoenberg68a? %Schoenberg69c % sonya \rhl{S} \refJ Schoenberg, I. J.; Cardinal interpolation and spline functions; \JAT; 2; 1969; 167--206; %Schoenberg69d % carl 22may98 \rhl{S} \refB Schoenberg{ (ed.)}, I. J.; Approximation with Special Emphasis on Spline Functions; Academic Press (New York); 1969; %Schoenberg70a % larry \rhl{S} \refJ Schoenberg, I. J.; A second look at approximate quadrature formulae and spline interpolation; \AiM; 4; 1970; 277--300; %Schoenberg71b % larry 29apr97 \rhl{S} \refJ Schoenberg, I. J.; On equidistant cubic spline interpolation; \BAMS; 77; 1971; 1039--1044; % MRC Rept.\ 1121: june 1971: On cubic spline interpolation at equidistant nodes %Schoenberg71d % . \rhl{S} \refJ Schoenberg, I. J.; The perfect B-splines and a time-optimal control problem; \IsJM; 10; 1971; 261--274; %Schoenberg71e % author 29apr97 \rhl{S} \refQ Schoenberg, I. J.; On polynomial spline functions on the circle. I and II; (Proceedings of the Conference on Constructive Theory of Functions), xxx (ed.), Hungarian Acad.\ Sci.{} (Budapest); 1971; 403--433; %Schoenberg72a % larry \rhl{S} \refJ Schoenberg, I. J.; Cardinal interpolation and spline functions: II. Interpolation of data of power growth; \JAT; 6; 1972; 404--420; %Schoenberg72b \rhl{S} \refR Schoenberg, I. J.; Notes on spline functions II. On the smoothing of histograms; University of Wisconsin-Madison, Mathematics Research Center, Rpt.\ \# 1222; 1972; %Schoenberg72d % author 29apr97 \rhl{S} \refP Schoenberg, I. J.; Cardinal interpolation and spline functions IV. The exponential Euler splines; \ButzerI; 382--404; % MRC TSR 1153, dec71 %Schoenberg72e % author 29apr97 \rhl{S} \refJ Schoenberg, I. J.; Notes on spline functions I. The limits of the interpolating periodic spline functions as their degree tends to infinity; Indag.\ Math.; 34(5); 1972; 412--422; % MRC TSR 1219, 1972 %Schoenberg73a \rhl{S} \refB Schoenberg, I. J.; Cardinal Spline Interpolation; Vol.~12, CBMS, SIAM (Philadelphia); 1973; %Schoenberg73b % carl NOTE: former 73b also exists, completed, as 73c \rhl{S} \refJ Schoenberg, I. J.; List of Publications of I. J. Schoenberg; \JAT; 8; 1973; x--xiv; %Schoenberg73c \rhl{S} \refP Schoenberg, I. J.; Splines and histograms (with an Appendix by C. de Boor); \EdmontonI; 277--327; %Schoenberg73d % carl \rhl{S} \refJ Schoenberg, I. J.; Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity; \IsJM; 16; 1973; 87--93; % follow-up on Golitschek72 %Schoenberg73e % carl 22may98 \rhl{S} \refJ Schoenberg, I. J.; The elementary cases of Landau's problem of inequalities between derivatives; \AMMo; 80; 1973; 121--158; % MRC TSR 1147, feb72 author has % The elementary cases of Landau's inequality between derivatives %Schoenberg74a % . 5dec96 \rhl{S} \refJ Schoenberg, I. J.; Cardinal interpolation and spline functions VI. Semi-cardinal interpolation and quadrature formulae; \JAM; XXVII; 1974; 159--204; % MRC Rpt.\ \# 1180: 1971: %Schoenberg74b % carl \rhl{S} \refJ Schoenberg, I. J.; Cardinal interpolation and spline functions VII. The behavior of cardinal spline interpolation as their degree tends to infinity; \JAM; XXVII; 1974; 205--229; %Schoenberg74c % author 05feb96 \rhl{S} \refQ Schoenberg, I. J.; Spline functions and differential equations -- First order equations; (Studies in Numerical Analysis), B.K.P. Scaife (ed.), Academic Press (London); 1974; 311--324; % Spline functions and differential equations I. First order equations; % University of Wisconsin-Madison, Mathematics Research Center, Rpt.\ \# % 1267: 1972: % see Schoenberg72c %Schoenberg75a % author 20feb96 \rhl{S} \refJ Schoenberg, I. J.; Notes on spline functions V. Orthogonal or Legendre splines; \JAT; 13; 1975; 84--104; % UW Mathematics Research Center, Rpt.\ \#1360: 1973: %Schoenberg76a % author 29apr97 \rhl{S} \refP Schoenberg, I. J.; On remainders and the convergence of cardinal spline interpolation for almost periodic functions; \Karlin; 277--303; % MRC TSR 1514, dec74 %Schoenberg76b % author 29apr97 \rhl{S} \refP Schoenberg, I. J.; On Charles Micchelli's theory of cardinal L-splines; \Karlin; 251--276; % MRC TSR 1511, dec74 %Schoenberg76c % author 20jun97 \rhl{S} \refQ Schoenberg, I. J.; The Landau problem of the differential operator $D^2 - \alpha^2$ in a circular ring; (Fourier Analysis and Approximation Theory), xxx (ed.), Colloquia Mathematica Societatis Janos Bolyai, 19, (Budapest); 1976; 713--723; %Schoenberg76d % author 29apr97 \rhl{S} \refP Schoenberg, I. J.; Notes on spline functions VI. Extremum problems of the Landau-type for the differential operators $D^2\pm1$; \Karlin; 353--368; % MRC TSR 1423, 1974 %Schoenberg77 % . 20jun97 \rhl{S} \refQ Schoenberg, I. J.; On cardinal spline smoothing; (Proc.\ Internat.\ Symp.\ Approx.\ Theory, Campinas, Brazil), J. B. Prolla (ed.), North-Holland Publ., Doordrecht (Holland); 1979; 383--407; % mrc tsr 1914 %Schoenberg77a % author 20jun97 \rhl{S} \refJ Schoenberg, I. J.; Approximating lengths, areas and volumes by polygons and polyhedra; Delta; 7; 1977; 32--46; %Schoenberg77b % . 20jun97 \rhl{S} \refJ Schoenberg, I. J.; The Landau problem for motions in a ring and in bounded continua; \AMMo; 84; 1977; 1--12; % mrc tsr 1563, 1975. of polynomials; mrc tsr 2757; 1984; %Schoenberg77c % . 20jun97 \rhl{S} \refQ Schoenberg, I. J.; On the zeros of the successive derivatives of integral functions. II; (Complex Analysis, Kentucky 1976), J. D. Buchholz and T. J. Suffridge (eds.), Lecture Notes in Mathematics {\bf599}, Springer-Verlag (New York); 1977; 109--116; %Schoenberg78 % . 20jun97 \rhl{S} \refJ Schoenberg, I. J.; Extremum problems for the motions of a billiard ball. III: The multidimensional case of K\"onig and Szucs; \SM; 13; 1978; 53--78; % mrc tsr 1880 %Schoenberg83a % . 20jun97 \rhl{S} \refJ Schoenberg, I. J.; Interpolating splines as limits of polynomials; \LAA; 52/53; 1983; 617--628; % mrc tsr 2234, 1981. %Schoenberg83b % . 20jun97 \rhl{S} \refJ Schoenberg, I. J.; A new approach to Euler splines; \JAT; 39; 1983; 324--337; %Schoenberg84a % . 20jun97 \rhl{} \refR Schoenberg, I. J.; On the spans of polynomials and the spans of a Laguerre-Polya-Schur sequence of polynomials; MRC Technical Summary Report \#2757; 1984; %Schoenberg84b % . 20jun97 \rhl{S} \refQ Schoenberg, I. J.; Euler's contribution to cardinal spline interpolation: The exponential Euler spline; (Leonhardt Euler 1707--1783, Beitr\"age zu Leben und Werk), xxx (ed.), Birkh\"auser (Basel); 1984; 199--213; \JAT; 39; 1983; 324--337; %Schoenberg84c % . 20nov03 \rhl{} \refR Schoenberg, I. J.; On the quadratic mean radius of a polynomial in $\CC[z]$; MRC Technical Summary Report \#2773; 1984; %Schoenberg84d % . 20nov03 \rhl{} \refR Schoenberg, I. J.; On a theorem of Szeg\H o on univalent convex maps of the unit circle; MRC Technical Summary Report \#2647; 1984; %Schoenberg88 % carl 12mar97 \rhl{S} \refB Schoenberg, I. J.; Selected Papers, Vols.\ 1 \& 2; C. de Boor (ed.), Birkh\"auser (Basel); 1988; % ISBN 3-7643-3378-2 , ISBN 3-7643-3405-3 %Schoenberg88b \rhl{} 20nov03 \refJ Schoenberg, I. J.; The Chinese remainder problem and polynomial interpolation; College Math.{} J.; 18(4); 1988; 320--322; %SchoenbergCavaretta72 \rhl{S} \refP Schoenberg, I. J., Cavaretta, A.; Solution of Landau's problem concerning higher derivatives on the halfline; \VarnaI; 297--308; % University of Wisconsin-Madison, Mathematics Research Center, Rpt.\ \# % 1050: 1970: %SchoenbergSharma71 % sherm \rhl{S} \refJ Schoenberg, I. J., Sharma, A.; The interpolatory background of the Euler-Maclaurin quadrature formula; \BAMS; 77; 1971; 1034--1038; %SchoenbergSharma73 % larry \rhl{S} \refJ Schoenberg, I. J., Sharma, A.; Cardinal Interpolation and spline functions V. The B-splines for cardinal Hermite interpolation; \LAA; 7; 1973; 1--42; %SchoenbergSilliman74 % sherm, carl \rhl{S} \refJ Schoenberg, I. J., Silliman, S. D.; On semi-cardinal quadrature formulae; \MC; 28(126); 1974; 483--497; % extended abstract in \TexasI: 461--467: %SchoenbergWhitney49 \rhl{S} \refJ Schoenberg, I. J., Whitney, A.; Sur la positivit\'e des d\'eterminants de translations des fonctions de fr\'equence de P\'olya avec une application a une probl\`eme d'interpolation; \CRASP Ser.\ A; 228; 1949; 1996--1998; %SchoenbergWhitney53a % . 19may96 \rhl{S} \refJ Schoenberg, I. J., Whitney, A.; On P\'olya frequency functions.\ III. The positivity of translation determinants with an application to the interpolation problem by spline curves; \TAMS; 74; 1953; 246--259; %SchoenbergZiegler70 % larry \rhl{S} \refJ Schoenberg, I. J., Ziegler, Z.; On cardinal monosplines of least $L_{\infty}$-norm on the real axis; \JAM; 23; 1970; 409--436; %Schomberg73 % werner 26aug98 \rhl{S} \refD Schomberg, H.; Tschebyscheff-Approximation durch rationale Splinefunktionen mit freien Knoten; M\"unster (Germany); 1973; % free knots: see Werner79a %Schonefeld68 \rhl{S} \refR Schonefeld, S.; Schauder bases in spaces of differentiable functions; 586--590; 1968; %Schonhage71 \rhl{S} \refB Sch\"onhage, A.; Approximationstheorie; de Gruyter (Berlin); 1971; %Schonhardt28 \rhl{S} \refJ Sch\"onhardt, E.; \"Uber die Zerlegung von Dreickspolyedern in Tetraeder; Math.\ Annal.; 98; 1928; 309--312; %Schonherr93 % author 08apr04 \rhl{} \refJ Schonherr, J.; Smooth biarc curves; \CAD; 25; 1993; 365--370; %Schreiner97 % carl 20jun97 \rhl{S} \refJ Schreiner, Michael; Locally supported kernels for spherical spline interpolation; \JAT; 89(2); 1997; 172--194; % (RKHS) reproducing kernel Hilbert spaces on the sphere with a locally % supported kernel. %Schultz69a % larry \rhl{S} \refP Schultz, M. H.; Multivariate spline functions and elliptic problems; \MadisonII; 279--347; %Schultz69b % sonya \rhl{S} \refJ Schultz, M. H.; Multivariate $L-$spline interpolation; \JAT; 2; 1969; 127--135; %Schultz69c % carl \rhl{S} \refJ Schultz, Martin H.; $L^\infty$ multivariate approximation theory; \SJNA; 6; 1969; 161--183; %Schultz69d % carl \rhl{S} \refJ Schultz, Martin H.; $L^2$ multivariate approximation theory; \SJNA; 6; 1969; 184--209; %Schultz69e % larry \rhl{S} \refJ Schultz, Martin H.; $L\sp{2}$-approximation theory of even order multivariate splines; \SJNA; 6; 1969; 467--475; %Schultz69f % larry \rhl{S} \refJ Schultz, M. H.; Approximation theory of multivariate spline functions in Sobolev spaces; \SJNA; 6; 1969; 570--582; %Schultz70 % larry, carl \rhl{S} \refJ Schultz, Martin H.; Elliptic spline functions and the Rayleigh-Ritz-Galerkin method; \MC; 24(109); 1970; 65--80; % variational method, spline space, two-point boundery value problem, % spline interpolation. %Schultz70a % larry \rhl{S} \refJ Schultz, M. H.; Elliptic spline functions and the Rayleigh-Ritz-Galerkin method; \MC; 24; 1970; 65--80; %Schultz70b % carl \rhl{S} \refJ Schultz, Martin H.; Error bounds for polynomial spline interpolation; \MC; 24(111); 1970; 507--515; %Schultz71 % larry \rhl{S} \refJ Schultz, M. H.; $L^2$ error bounds for the Rayleigh-Ritz-Galerkin method; \SJNA; 8; 1971; 737--748; %Schultz72 \rhl{S} \refJ Schultz, Martin H.; Discrete Tchebycheff approximation for multivariate splines; J. Comput.\ System Sci.; 6; 1972; 298--304; %Schultz73b \rhl{S} \refB Schultz, M. H.; Spline Analysis; Prentice--Hall (Englewood Cliffs, NJ); 1973; %Schultz73c % sonya \rhl{S} \refJ Schultz, M. H.; Error bounds for a bivariate interpolation scheme; \JAT; 8; 1973; 189--194; %SchultzVarga67 % larry \rhl{S} \refJ Schultz, M. H., Varga, R. S.; $L$-splines; \NM; 10; 1967; 345--369; %Schulze89 % larry \rhl{S} \refP Schulze, G.; Segmentation operators on Coons' patches; \Oslo; 561--572; % Guido Brunnett %Schumaker68a % larry \rhl{S} \refJ Schumaker, L. L.; Representation theorems for certain classes of generalized polynomials induced by Tchebycheff systems and applications to extremal problems; \JAM; 21; 1968; 313--335; %Schumaker68b % larry \rhl{S} \refJ Schumaker, L. L.; Uniform approximation by Tchebycheffian spline functions, II. Free knots; \SJNA; 5; 1968; 647--656; %Schumaker69a % larry \rhl{S} \refJ Schumaker, L. L.; Uniform approximation by Tchebycheffian spline functions; \JMM; 18; 1969; 369--377; %Schumaker69a % larry \rhl{S} \refP Schumaker, L. L.; Approximation by splines; \MadisonI; 65--85; %Schumaker69b % larry \rhl{S} \refP Schumaker, L. L.; Some algorithms for the computation of interpolating and approximating spline functions; \MadisonI; 87--102; %Schumaker69d % larry \rhl{S} \refJ Schumaker, L. L.; On the smoothness of best spline approximation; \JAT; 2; 1969; 410--418; %Schumaker70 % larry \rhl{S} \refQ Schumaker, L. L.; A constrained rational approximation problem in filter design; (Proc.\ of the International Conference on Constructive Function Theory), xxx (eds.), Bulgarian Academy of Sciences (Sofia); 1970; 309--314; %Schumaker73a % larry \rhl{S} \refP Schumaker, L. L.; Constructive aspects of discrete polynomial spline functions; \TexasI; 469--476; %Schumaker76a % larry \rhl{S} \refP Schumaker, L. L.; Toward a constructive theory of generalized spline functions; \BoehmerII; 265--331; %Schumaker76b % larry \rhl{S} \refP Schumaker, L. L.; Fitting surfaces to scattered data; \TexasII; 203--268; %Schumaker76c % larry \rhl{S} \refP Schumaker, L. L.; Two-stage methods for fitting surfaces to scattered data; \BonnI; 378--389; %Schumaker76d % larry \rhl{S} \refJ Schumaker, L. L.; Zeros of spline functions and applications; \JAT; 18; 1976; 152--168; %Schumaker76e % larry \rhl{S} \refJ Schumaker, L. L.; On Tchebychevian spline functions; \JAT; 18; 1976; 278--303; %Schumaker78 % larry \rhl{S} \refR Schumaker, L. L.; Lower bounds for spline approximation; Banach Center Publ.\ 4, Z. Ciesielski, (ed.), 1978; 213--223; %Schumaker79a % larry \rhl{S} \refP Schumaker, L. L.; On the dimension of spaces of piecewise polynomials in two variables; \MvatI; 396--412; %Schumaker79b % larry \rhl{S} \refQ Schumaker, L. L.; $L_2$ approximation by splines with free knots; (Approximation in Theorie und Praxis), G. Meinardus (ed.), Bibliographisches Inst.\ (Mannheim); 1979; 157--182; %Schumaker81a % larry \rhl{S} \refB Schumaker, L. 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